Problem #$5(20$ marks$4($a$)-10$marks, $($b$)-10$marks$)$ A unity feedback system has a plant transfer function given by: $)1(1)(+=$ ss p sG $($a$)$ Using root$-$locus method $($based on characteristic equation$),$ design a cascade proportional derivative $($PD$)$ compensator asKsG $)()($ c $+=$ so that the following design specifications are met: Percent overshoot OP $=\%32\mathrm{.}4..$ Natural frequency $$n $=$ rad sec$/07\mathrm{.}7($b$)$ Using root$-$locus method $($based on characteristic equation$),$ design a cascade